and \(p_\theta \)  is the density function corresponding to \(P_\theta \) . The problem, of course, is that \(V_{\theta ^\dagger }^{-1}\)  is not the asymptotic covariance matrix of \(\hat{\theta }_n\) ; the latter, as shown by [1]} and [2]}, has the famous sandwich formula \(V_{\theta ^\dagger }^{-1} \Lambda _{\theta ^\dagger } V_{\theta ^\dagger }^{-1}\) , where
\( \Lambda _{\theta ^\dagger } = \int \Bigl ( \frac{\partial \log p_\theta }{\partial \theta } \Bigr |_{\theta =\theta ^\dagger } \Bigr ) \Bigl ( \frac{\partial \log p_\theta }{\partial \theta } \Bigr |_{\theta =\theta ^\dagger } \Bigr )^\top \, dP^\star . \) 
